from prefect import task, Flow, Parameter
from prefect.engine.signals import FAIL, SKIP

def custom_trigger(upstream_states):
    if any(isinstance(s.result, FAIL) for s in upstream_states):
        return False
    else:
        return True

@task(trigger=custom_trigger)
def my_task():
    print('running')

@task
def upstream(x):
    if x == 1:
        raise FAIL("1")
    else:
        raise SKIP("other")

with Flow("example") as flow:
    x = Parameter("x", default=1)
    result = my_task(upstream_tasks=[upstream(x)])

flow.run() # fails
flow.run(x=0) # succeeds